context listlengths 1 1 | gen_kwargs dict | repeat_idx int64 0 9 | request_idx int64 0 514 | task_name stringclasses 12
values | metadata dict | model_outputs stringlengths 1 246k |
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[
{
"content": "Problem: There are $n$ values of $x$ in the interval $0<x<2\\pi$ where $f(x)=\\sin(7\\pi\\cdot\\sin(5x))=0$. For $t$ of these $n$ values of $x$, the graph of $y=f(x)$ is tangent to the $x$-axis. Find $n+t$.\nMark your solution with \\boxed\nAnswer:",
"role": "user"
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"seed": 9,
"temperature": 0.7
} | 9 | 23 | AIME25 | {
"expected_answer": "149",
"problem_id": "II-9",
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} | To solve the problem, we need to determine the number of values \( n \) where \( f(x) = \sin(7\pi \cdot \sin(5x)) = 0 \) in the interval \( 0 < x < 2\pi \), and the number of these \( n \) values where the graph of \( y = f(x) \) is tangent to the \( x \)-axis. Then, we need to compute \( n + t \).
### Step 1: Find \(... |
[
{
"content": "\"You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print th... | {
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"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 88 | CodeElo | {
"expected_answer": "",
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} | Okay, I need to solve this problem where I have to count the number of possible nonempty strings t (other than 'a') that can partition the given string s into substrings. Each substring must be either t or 'a', and at least one substring is t. So the problem is to find all possible t's that meet these conditions.
Let ... |
[
{
"content": "\"You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print th... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 40 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_rationale": null,
"reference_solution": "",
"subject": null,
"type": null
} | Okay, let's try to figure out this problem. So, we need to find the number of permutations of size n that can be split into q operations as described, resulting in the given l and r sequences. Hmm.
First, let's understand the problem with the example given. The initial array is [6,3,4,1,2,5]. The first split gives two... |
[
{
"content": "You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print the ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 104 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_rationale": null,
"reference_solution": "",
"subject": null,
"type": null
} | Okay, let's try to understand the problem. So, we have a matrix with two rows and n columns. We can swap any two columns any number of times. After swapping, we need to find a path from (1,1) to (2,n) that goes through the cells. The path can move right or down at each step. The cost is the sum of all cells in the path... |
[
{
"content": "\"You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print th... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 378 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_rationale": null,
"reference_solution": "",
"subject": null,
"type": null
} | Okay, let's tackle this problem. So the goal is to construct a permutation of numbers 1 to n such that after performing the operations (bitwise AND for odd steps, OR for even steps), the final k is maximized. Hmm.
First, I need to understand the process step by step. Let's break down the operations:
For each i from 1... |
[
{
"content": "\"You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print th... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 49 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_rationale": null,
"reference_solution": "",
"subject": null,
"type": null
} | Okay, let's tackle this problem step by step. So, the goal is to find for each candidate i the minimum number of candidates that need to be excluded so that candidate i wins. Hmm.
First, let's understand the problem thoroughly. The candidates are numbered from 1 to n. Each has a certain number of fans a_i. Additionall... |
[
{
"content": "Your response should be in the following format:\nExplanation: {your explanation for your answer choice}\nAnswer: {your chosen answer}\nConfidence: {your confidence score between 0% and 100% for your answer}\nEffective antibody production by B cells of the mammalian adaptive immune system is criti... | {
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"max_new_tokens": 32768,
"seed": 2,
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} | 2 | 120 | HLESubset | {
"expected_answer": "B",
"problem_id": "670013827794cc36bc974f27",
"reference_rationale": "B cell production of high-affinity antibodies requires class-switching and somatic hypermutation (SHM). For the induction of an adaptive immune response as well as high-affinity antibody production against a target antigen... | Explanation: The question asks which groups of mice (G1 to G6) would have a significantly different titer of high-affinity OVA-specific antibodies that have undergone somatic hypermutation (SHM) compared to wild-type mice. The answer requires an understanding of how each genetic mutation or knockout affects the adaptiv... |
[
{
"content": "Your response should be in the following format:\nExplanation: {your explanation for your answer choice}\nAnswer: {your chosen answer}\nConfidence: {your confidence score between 0% and 100% for your answer}\nTo improve the catalytic efficiency of enzyme Zma1, which converts molecule A to B resear... | {
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"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 223 | HLESubset | {
"expected_answer": "G",
"problem_id": "671d9e9d29e7fde7166e474d",
"reference_rationale": "1. Metals.\nIt is known that divalent metal ions function as cofactors of enzymes.\nThe presence of MgCl2 increases kcat so MgCl2 is a cofactor.\nCucl2 and Cacl2 decrease kcat so CuCl2 and CaCl2 are inhibitors. Cu ions and... | Explanation:
The key to answering this question lies in understanding the effect of various compounds on the enzyme's catalytic efficiency (kcat) and their known roles in enzymology.
Looking at the data:
- When Al1 is added, the kcat increases to 1000/second, which is a significant increase compared to the control... |
[
{
"content": "Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.You are given positive integers N, M, K, and a sequence of non-negative integers: A=(A_1,A_2,\\ldots,A_N).\nFor a non-... | {
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"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 111 | LiveCodeBenchV5 | {
"expected_answer": "",
"problem_id": "",
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"subject": null,
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} | To solve this problem, we need to compute the sum of the scores of all non-empty subsequences of the given array A. The score of a subsequence is defined based on its length. If the length is a multiple of M, the score is the XOR of all elements in the subsequence raised to the power K. Otherwise, the score is 0. The r... |
[
{
"content": "In this problem, multiple options can be correct. Give a detailed solution and end the solution with the final answer. Mark your solution, which should be one or more multiple-choice letter(s), with \\boxed\nAnswer:\n\nProblem: The circle $C_{1}: x^{2}+y^{2}=3$, with centre at $O$, intersects the ... | {
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"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 35 | JEEBench | {
"expected_answer": "ABC",
"problem_id": "48",
"reference_rationale": null,
"reference_solution": null,
"subject": "math",
"type": "MCQ(multiple)"
} | To solve this problem, we need to determine the coordinates of point \( P \) where the circle \( C_1 \) intersects the parabola \( x^2 = 2y \) in the first quadrant. Then, find the equations of the tangent lines to \( C_1 \) at \( P \), and determine the coordinates of the centers \( Q_2 \) and \( Q_3 \) of circles \( ... |
[
{
"content": "Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.There is a rectangular cake with some strawberries on the xy-plane. The cake occupies the rectangular area \\lbrace (x... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 210 | LiveCodeBench | {
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} | To solve this problem, we need to determine the minimum and maximum number of strawberries that can be found in any of the resulting rectangular pieces after cutting the cake with given vertical and horizontal lines.
### Approach
1. **Identify the Regions**: The cake is divided into several rectangles by A vertical l... |
[
{
"content": "\"You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print th... | {
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"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 198 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_rationale": null,
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} | Okay, let's tackle this problem. Hmm. So the problem is about checking if a string matches a numeric template. The conditions are a bit tricky. Let's break them down.
First, the string's length must equal the number of elements in the array. That's straightforward. So for each test case, the first thing is to check if... |
[
{
"content": "In this problem, the final will be a numeric value. Give the numerical answer correct upto the 2nd decimal digit. Give a detailed solution and end the solution with the final answer. Mark your solution with \\boxed\nAnswer:\n\nProblem: At $298 \\mathrm{~K}$, the limiting molar conductivity of a we... | {
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"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 353 | JEEBench | {
"expected_answer": "0.22",
"problem_id": "25",
"reference_rationale": null,
"reference_solution": null,
"subject": "chem",
"type": "Numeric"
} | Alright, let's tackle this problem step by step. It's about the dissociation of a weak monobasic acid in water, and we need to find the degree of dissociation, α, given some conditions about molar conductivity before and after dilution.
First, let's recall some fundamental concepts. For a weak electrolyte, the molar ... |
[
{
"content": "Generate an executable Python function generated from the given prompt. Return the function body without invoking it at the final solution.You are given an array of integers nums. Some values in nums are missing and are denoted by -1.\nYou can choose a pair of positive integers (x, y) exactly once... | {
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"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 324 | LiveCodeBenchV5 | {
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} | To solve this problem, we need to minimize the maximum absolute difference between adjacent elements in an array where some elements are missing and denoted by -1. We can replace each missing element with either of two positive integers (x, y) exactly once. The goal is to find the optimal (x, y) pair that results in th... |
[
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"content": "\"You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print th... | {
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} | 1 | 87 | CodeElo | {
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} | Okay, let's tackle this problem. Hmm. The problem is about finding the number of ways to choose between option 1 and 2 for each element in the array such that the final value of c is maximized. Then, we need to count how many distinct paths lead to that maximum value.
First, I need to understand what the maximum possi... |
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"content": "Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.There is a weighted simple directed graph with N vertices and M edges.\r\nThe vertices are numbered 1 to N, and the i-... | {
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} | 0 | 374 | LiveCodeBench | {
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} | To solve this problem, we need to determine if there's a walk that visits every vertex at least once in a directed graph. If such a walk exists, we need to find the minimum total weight of the edges traversed. If not, we should output "No".
### Approach
The problem can be approached using dynamic programming (DP) comb... |
[
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"content": "In this problem, only one option will be correct. Give a detailed solution and end the solution with the final answer. Mark your solution, which should be exactly one multiple-choice letter, with \\boxed\nAnswer:\n\nProblem: A debate club consists of 6 girls and 4 boys. A team of 4 members is to b... | {
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"seed": 1,
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} | 1 | 25 | JEEBench | {
"expected_answer": "A",
"problem_id": "38",
"reference_rationale": null,
"reference_solution": null,
"subject": "math",
"type": "MCQ"
} | To solve this problem, we need to determine the number of ways to select a team of 4 members from a debate club consisting of 6 girls and 4 boys, with the condition that the team includes at most one boy. Additionally, one of these 4 members must be designated as the captain.
First, let's break down the problem into ... |
[
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"content": "\"You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print th... | {
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"seed": 1,
"temperature": 0.7
} | 1 | 63 | CodeElo | {
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} | Okay, let's tackle this problem. Hmm. The problem is about dividing a grid into two parts such that Alice's part includes cell (n,1) and Bob's includes (1,m). The goal is to maximize the size of Alice's part when Bob doesn't give her any fountains, and then compute the maximum gain for each fountain if it's given to Al... |
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"content": "You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print the ... | {
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} | 0 | 351 | CodeForces | {
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} | Okay, let's tackle this problem step by step. So, the problem is about a tree where some nodes have 0, 1, or ? as their values. The game is between Iris and Dora, where they take turns assigning the ? values, with Iris going first. The goal is to compute the score of the tree, which is the number of leaves that have a ... |
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"content": "In this problem, multiple options can be correct. Give a detailed solution and end the solution with the final answer. Mark your solution, which should be one or more multiple-choice letter(s), with \\boxed\nAnswer:\n\nProblem: Which of the following statement(s) is(are) true?\n(A) Monosaccharides... | {
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} | 2 | 196 | JEEBench | {
"expected_answer": "ACD",
"problem_id": "29",
"reference_rationale": null,
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"subject": "chem",
"type": "MCQ(multiple)"
} | Alright, let's tackle each of these statements one by one. I'll go through each option carefully, explain my reasoning, and then conclude with the correct answers.
Starting with option (A): "Monosaccharides cannot be hydrolysed to give polyhydroxy aldehydes and ketones."
First, let's recall what monosaccharides are. ... |
[
{
"content": "Your response should be in the following format:\nExplanation: {your explanation for your answer choice}\nAnswer: {your chosen answer}\nConfidence: {your confidence score between 0% and 100% for your answer}\nTwo business partners named Alex and Tyler are looking to incorporate a company in Ontari... | {
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"max_new_tokens": 32768,
"seed": 1,
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} | 1 | 216 | HLESubset | {
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"problem_id": "671c6a1aacee876e82d4bc0e",
"reference_rationale": "This questions deals with incorporations and corporate structuring, and presents a type of matter that is very common. For the purposes of keeping the answer options a reasonable length, only the three rights that are req... | Explanation: Let's analyze each option to see which one satisfies all the requirements.
First, requirement 1: Equal control over the company. This means that both partners should have equal voting rights. Requirement 2: Alex wants salary payments, which likely means his shares should not pay dividends. Requirement 3: ... |
[
{
"content": "Return your final response within \\boxed{{}} and only include the letter choice (A, B, C, D, E, F, G, H, I, or J) as your final response.\nProblem: There are three main types of buying situations in an organization, referred to by Robinson, Faris, and Wind (1967) as _____________.\nOptions: A. B... | {
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} | J
The problem refers to three main types of buying situations in an organization as defined by Robinson, Faris, and Wind in 1967. After reviewing the options, the term that best fits this description is "Buyclasses." This term aligns with the classification of different types of purchasing situations or categories wit... |
[
{
"content": "Generate an executable Python function generated from the given prompt. Return the function body without invoking it at the final solution.You are given three positive integers num1, num2, and num3.\nThe key of num1, num2, and num3 is defined as a four-digit number such that:\n\nInitially, if any ... | {
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"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 184 | LiveCodeBenchV5 | {
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"problem_id": "",
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} | To solve this problem, we need to generate a four-digit key based on the minimum digits from three given numbers. Each number is padded with leading zeros to ensure it is at least four digits long. Then, for each digit position (from the first to the fourth), we find the smallest digit among the corresponding digits of... |
[
{
"content": "Return your final response within \\boxed{{}} and only include the letter choice (A, B, C, D, E, F, G, H, I, or J) as your final response.\nProblem: What is the average kinetic energy of air molecules at a temperature of 300° K? What would be a typical speed for nitrogen molecules, which are the m... | {
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} | A
The average kinetic energy of air molecules at a temperature of 300 K can be calculated using the formula:
KE = (3/2) k_B T
where k_B is Boltzmann's constant, approximately 1.38 × 10^-23 J/K, and T is the temperature in Kelvin. Plugging in the values:
KE = (3/2) × 1.38 × 10^-23 J/K × 300 K = (1.035 × 10^-21 J/K) ... |
[
{
"content": "Your response should be in the following format:\nExplanation: {your explanation for your answer choice}\nAnswer: {your chosen answer}\nConfidence: {your confidence score between 0% and 100% for your answer}\nGiven that some environmental conditions of chronic infections favor the emergence of hyp... | {
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"max_new_tokens": 32768,
"seed": 1,
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} | 1 | 473 | HLESubset | {
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"problem_id": "673a8c2e4e2e35b51a27fafd",
"reference_rationale": "Conversion to the mucoid phenotype in hypermutator strains of Pseudomonas aeruginosa can be increased because of an increased mutation frequency on the mucA gene. However, most of mutations of the mucA gene observed in hyp... | Explanation: Hypermutator strains of Pseudomonas aeruginosa have a higher rate of mutation compared to their non-hypermutator counterparts. This increased mutation rate can lead to a higher diversity of genetic changes within the population. In the context of chronic infections, where environmental conditions favor the... |
[
{
"content": "Problem: Find the greatest common divisor of $3339$, $2961$, and $1491$.\nMark your solution with \\boxed\nAnswer:",
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}
] | {
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} | 0 | 89 | MATH500 | {
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} | To find the greatest common divisor (GCD) of 3339, 2961, and 1491, we can use the Euclidean algorithm. Let's proceed step by step.
First, we find the GCD of 3339 and 2961.
1. Compute GCD(3339, 2961):
- Apply the Euclidean algorithm:
- Divide 3339 by 2961. The quotient is 1, remainder 378 (3339 - 2961*1 = 378)... |
[
{
"content": "\"You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print th... | {
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"seed": 0,
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} | 0 | 25 | CodeElo | {
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} | Okay, let's tackle this problem. So, the problem is about a game between Alice and Bob where they take turns cutting rows or columns from a grid and collecting points based on the chips that are in the cut area. The challenge is to compute the total points each player gets after all moves are made.
Hmm. Let's start by... |
[
{
"content": "Problem: Find the number of ordered pairs $(x,y)$, where both $x$ and $y$ are integers between -100 and 100, inclusive, such that $12x^2 - xy - 6y^2 = 0$.\nMark your solution with \\boxed\nAnswer:",
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}
] | {
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} | 4 | 3 | AIME25 | {
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} | To solve the problem of finding the number of ordered pairs \((x, y)\) where both \(x\) and \(y\) are integers between -100 and 100, inclusive, such that \(12x^2 - xy - 6y^2 = 0\), we can proceed as follows:
First, we need to find all integer solutions \((x, y)\) to the equation:
\[
12x^2 - xy - 6y^2 = 0
\]
We can s... |
[
{
"content": "\"You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print th... | {
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"seed": 1,
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} | Okay, let's tackle this problem. Hmm. The problem is about finding the maximum number of times we can perform an operation on an array. The operation involves selecting an index i where a[i] equals i, then removing a[i] and a[i+1]. We need to do this optimally to maximize the number of operations.
So, the key here is ... |
[
{
"content": "Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.There are N cities in a certain country.\nYou will travel from your office in city 1 to a destination in city N, via z... | {
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"seed": 1,
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} | 1 | 309 | LiveCodeBench | {
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} | To solve this problem, we need to find the minimum time to travel from city 1 to city N using either a company car or a train, switching between them in cities. The key is to model this as a shortest path problem where each city can be a node, and edges represent the time taken to travel between cities via either mode ... |
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"content": "Return your final response within \\boxed{} and only include the letter choice (A, B, C, or D) as your final response.\nProblem: What is the energy of the Relativistic Heavy Ion Collider (RHIC) so that the speed of the nucleus X is equal to 0.96c?\n\nKnowing that X is defined as Li with 3 neutrons... | {
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} | A) 23.069 GeV
I used the formula for relativistic kinetic energy, which is K = (gamma - 1) * m_0 * c^2, where gamma is the Lorentz factor. For gamma = 1 / sqrt(1 - v^2/c^2), and given v = 0.96c. I calculated gamma as approximately 3.762. The rest mass energy of Li with 3 neutrons would be the sum of the masses of its ... |
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"content": "Problem: Let $p(x)$ be a monic polynomial of degree 4. Three of the roots of $p(x)$ are 1, 2, and 3. Find $p(0) + p(4).$\nMark your solution with \\boxed\nAnswer:",
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} | Given that \( p(x) \) is a monic polynomial of degree 4 with roots 1, 2, and 3, we need to find \( p(0) + p(4) \).
Since \( p(x) \) is monic and of degree 4, it can be written in the form:
\[
p(x) = (x - 1)(x - 2)(x - 3)(x - a)
\]
where \( a \) is the fourth root of the polynomial.
To find \( p(0) \) and \( p(4) \), ... |
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"content": "Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.There are N+2 cells arranged in a row. Let cell i denote the i-th cell from the left.\nThere is one stone placed in ea... | {
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} | 1 | 25 | LiveCodeBenchV5 | {
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} | To solve this problem, we need to determine if we can transform the initial state of the stones (given by string S) into the target state (given by string T) using the allowed operations. If possible, we need to find the minimum number of operations required.
### Approach
The key insight here is to model the movement... |
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"content": "Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.For a positive integer k, the Pyramid Sequence of size k is a sequence of length (2k-1) where the terms of the sequenc... | {
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"seed": 2,
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} | 2 | 363 | LiveCodeBench | {
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} | To solve this problem, we need to determine the maximum size of a Pyramid Sequence that can be formed from a given sequence by performing allowed operations: decreasing elements by 1 or removing elements from the ends. The key is to find the longest possible sequence that starts with 1, increases up to a peak, and then... |
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"content": "Problem: Let $ABCD$ be a tetrahedron such that $AB=CD= \\sqrt{41}$ , $AC=BD= \\sqrt{80}$ , and $BC=AD= \\sqrt{89}$ . There exists a point $I$ inside the tetrahedron such that the distances from $I$ to each of the faces of the tetrahedron are all equal. This distance can be written in the ... | {
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"expected_answer": "104",
"problem_id": "aime24-28",
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"reference_solution": "Notice that \\(41=4^2+5^2\\), \\(89=5^2+8^2\\), and \\(80=8^2+4^2\\), let \\(A~(0,0,0)\\), \\(B~(4,5,0)\\), \\(C~(0,5,8)\\), and \\(D~(4,0,8)\\). Then the plane \\(BCD\\) has a normal\n\\begin{equation*}\n... | To solve the problem, we need to determine the distance from the incenter \( I \) of the tetrahedron \( ABCD \) to each face, which is given as \( \frac{m \sqrt{n}}{p} \). The values \( m \), \( n \), and \( p \) are then used to compute \( m + n + p \).
First, we note that the tetrahedron \( ABCD \) is symmetric with... |
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"content": "\"You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print th... | {
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} | Okay, let's tackle this problem. So, the goal is to find the maximum possible MEX by optimally adding x to elements of the array. Hmm. Let's think about what MEX is. The MEX is the smallest non-negative integer not present in the array. So, for example, if the array has 0, 1, 3, then the MEX is 2.
The key here is to f... |
[
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"content": "Problem: The parabola with equation $y = x^2 - 4$ is rotated $60°$ counterclockwise around the origin. The unique point in the fourth quadrant where the original parabola and its image intersect has $y$-coordinate $\\frac{a-\\sqrt{b}}{c}$, where $a$, $b$, and $c$ are positive integers, and $a$ and... | {
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"seed": 3,
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} | 3 | 8 | AIME25 | {
"expected_answer": "62",
"problem_id": "I-9",
"reference_rationale": null,
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} | To solve this problem, we need to determine the unique point in the fourth quadrant where the original parabola \( y = x^2 - 4 \) and its image after a 60° counterclockwise rotation around the origin intersect. The goal is to find the \( y \)-coordinate of this intersection point in the form \( \frac{a - \sqrt{b}}{c} \... |
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{
"content": "In this problem, the final will be a numeric value. Give the numerical answer correct upto the 2nd decimal digit. Give a detailed solution and end the solution with the final answer. Mark your solution with \\boxed\nAnswer:\n\nProblem: Let $a_{1}, a_{2}, a_{3}, \\ldots$ be a sequence of positive i... | {
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"problem_id": "50",
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"subject": "math",
"type": "Numeric"
} | To solve this problem, we need to determine the number of possible values of \( c \) such that the given equality holds for some positive integer \( n \). Let's break down the problem step by step.
### Step 1: Understanding the Sequences
1. **Arithmetic Progression (AP) Sequence \( a_n \)**:
- First term: \( a_1 = ... |
[
{
"content": "You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print the ... | {
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} | 0 | 83 | CodeForces | {
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} | Okay, let's tackle this problem. So, the task is to find the number of distinct non-degenerate right triangles that can be formed from three given points. The key here is to remember that a right triangle has one 90-degree angle, and the other two angles sum to 90 degrees. So, for three points to form a right triangle,... |
[
{
"content": "You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print the ... | {
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} | 1 | 163 | CodeForces | {
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} | Okay, so the problem is about calculating binomial coefficients according to a wrong formula. Wait, wait. Wait, the original formula is C(n, k) = C(n-1, k) + C(n-1, k-1). But here, the mistake is in the way the coefficients are computed. Wait, the problem statement says that the code uses the first formula (which is th... |
[
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"content": "Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.You are given a length-N sequence A=(A_1,A_2,\\dots,A_N) consisting of 0, 1, and 2,\r\nand a length-N string S=S_1S_2\... | {
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} | 1 | 231 | LiveCodeBench | {
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} | To solve this problem, we need to compute the sum of the mex values for all valid triplets (i, j, k) in the given sequences A and S. The mex for a triplet (i, j, k) is the smallest non-negative integer not present in A_i, A_j, and A_k. The triplet (i, j, k) is valid if the substring S_iS_jS_k equals "MEX".
### Approac... |
[
{
"content": "In this problem, the final will be a numeric value. Give the numerical answer correct upto the 2nd decimal digit. Give a detailed solution and end the solution with the final answer. Mark your solution with \\boxed\nAnswer:\n\nProblem: Reaction of $\\mathbf{x} \\mathrm{g}$ of $\\mathrm{Sn}$ with $... | {
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} | 1 | 355 | JEEBench | {
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} | To solve this problem, we need to determine the mass of tin (Sn) reacted, denoted as x grams, given the reaction steps and the mass of the resulting organic salt. The key steps involve understanding the reactions involved and using stoichiometry to relate the masses.
### Step-by-Step Solution:
1. **Understanding the ... |
[
{
"content": "Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.There are zero or more sensors placed on a grid of H rows and W columns. Let (i, j) denote the square in the i-th row ... | {
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} | To solve this problem, we need to determine the number of connected sensor clusters on a grid where sensors interact via adjacency (including diagonally adjacent). The key challenge is efficiently identifying and counting these clusters given the constraints of large grid sizes (up to 1000x1000).
### Approach
1. **Ide... |
[
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"content": "\"You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print th... | {
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} | Okay, let's tackle this problem. Hmm, the problem is to find the maximum possible sum of the GCDs of two arrays (after swapping a_i and b_i for any subset of elements, paying c_i coins for each swap) for various d values. The key here is to maximize the sum of the GCDs of the a array and the b array after swapping. So,... |
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"content": "Return your final response within \\boxed{{}} and only include the letter choice (A, B, C, D, E, F, G, H, I, or J) as your final response.\nProblem: Discuss thetonotopicorganization of our auditory system.\nOptions: A. Tonotopic organization describes the layout of taste buds on the tongue and the... | {
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} | 0 | 229 | MMLUPro | {
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The correct answer is B. Tonotopic organization refers to the spatial representation of tones in the brain and on the basilar membrane in the ear, enabling the brain to distinguish between different tones. This organization allows the auditory system to map different frequencies along the basilar membrane, with lowe... |
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{
"content": "Return your final response within \\boxed{{}} and only include the letter choice (A, B, C, D, E, F, G, H, I, or J) as your final response.\nProblem: A negative point charge of 10^-6 coulomb is situated in air at theorigin of a rectangular coordinate system. A second negativepoint charge of 10^-4 c... | {
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The force between two point charges is given by Coulomb's law: F = k * |q1*q2| / r^2, where k is Coulomb's constant (approximately 8.99 x 10^9 N·m²/C²), q1 and q2 are the magnitudes of the charges, and r is the distance between them.
In this case, both charges are negative, so the force between them will be attract... |
[
{
"content": "Your response should be in the following format:\nExplanation: {your explanation for your answer choice}\nAnswer: {your chosen answer}\nConfidence: {your confidence score between 0% and 100% for your answer}\nA surface current of infinite extent in the$y$ and $z$ directions, $\\vec{K}(x = 0, t) = ... | {
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} | 1 | 234 | HLESubset | {
"expected_answer": "B",
"problem_id": "671eeb53c1a668a6c81e5993",
"reference_rationale": "1. In the superconducting region, Maxwell's equations in their time-varying form are given by:\n$\\vec{J} = \\varepsilon_0 \\frac{\\partial \\vec{E}}{\\partial t}, \\quad \\nabla \\times \\vec{H} = \\varepsilon_0 \\omega_p... | Explanation: The problem involves determining the force per unit area on the $x = d$ plane in a complex electromagnetic configuration. The setup includes an infinite surface current in the $y$ and $z$ directions, located at $x = 0$, with regions of different materials: a region with infinite magnetic permeability ($\mu... |
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"content": "\"You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print th... | {
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} | 0 | 30 | CodeElo | {
"expected_answer": "",
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"subject": null,
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} | Okay, let's tackle this problem. Hmm. So the problem is about painting a tree with two chess pieces moving around. The goal is to find the minimum number of steps to paint all vertices blue. Let me try to understand the rules again.
So, initially, all vertices are white. Then, the two pieces start at a and b. Each ste... |
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{
"content": "Your response should be in the following format:\nExplanation: {your explanation for your answer choice}\nAnswer: {your chosen answer}\nConfidence: {your confidence score between 0% and 100% for your answer}\nWhat kind of conceptual metaphor is expressed by \"my love for humanity\", according to \... | {
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} | 1 | 128 | HLESubset | {
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"reference_rationale": "Lakoff and Johnson use the term 'physical metaphor' in this paper for the most common, almost undetectable type of metaphor used to make it possible to talk about abstract things in simpler terms such as 'the brutality of ... | Explanation: The phrase "my love for humanity" is an example of a conceptual metaphor. Conceptual metaphors are a type of metaphor that involves transferring the meaning of one concept to another by understanding the source domain in terms of the target domain. In this case, "love" is the source domain, and "humanity" ... |
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"content": "\"You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print th... | {
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} | 2 | 67 | CodeElo | {
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} | Okay, I need to solve this problem where I have to reconstruct a sequence based on some incomplete values. Let's think about how to approach this.
The problem says that for each i from 1 to n-1, either a_i = floor(a_{i+1}/2) or a_{i+1} = floor(a_i/2) must hold. But some elements are missing (-1). So the goal is to fil... |
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"content": "\"You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print th... | {
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"seed": 1,
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} | 1 | 92 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_rationale": null,
"reference_solution": "",
"subject": null,
"type": null
} | Okay, let's try to tackle this problem. Hmm, the problem is about capturing all towers by using certain operations. The goal is to find the number of minimal-length attack plans. Let's break this down.
First, the problem states that we start with two towers (the first and second given in the input). Then, each operati... |
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{
"content": "Generate an executable Python function generated from the given prompt. Return the function body without invoking it at the final solution.A truck has two fuel tanks. You are given two integers, mainTank representing the fuel present in the main tank in liters and additionalTank representing the f... | {
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} | 0 | 51 | LiveCodeBench | {
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} | To solve this problem, we need to calculate the maximum distance a truck can travel given two fuel tanks and specific fuel transfer rules. The truck has a mileage of 10 km per liter, and every time 5 liters are consumed from the main tank, if possible, 1 liter from the additional tank is transferred to the main tank. T... |
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"content": "In this problem, the final answer will be a non-negative integer. Give a detailed solution and end the solution with the final answer. Mark your solution with \\boxed\nAnswer:\n\nProblem: What is the sum of the number of lone pairs of electrons on each central atom in the following species?\n$\\le... | {
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} | 1 | 81 | JEEBench | {
"expected_answer": "6",
"problem_id": "28",
"reference_rationale": null,
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"subject": "chem",
"type": "Integer"
} | Okay, so I need to find the sum of the number of lone pairs on each central atom in these species: TeBr6²⁻, BrF2⁺, SNF3, and XeF3⁻. Let me break this down step by step.
First, I should recall that lone pairs are pairs of electrons on the central atom that are not involved in bonding with other atoms. To find the numb... |
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{
"content": "Problem: Torus $T$ is the surface produced by revolving a circle with radius $3$ around an axis in the plane of the circle that is a distance $6$ from the center of the circle (so like a donut). Let $S$ be a sphere with a radius $11$ . When $T$ rests on the inside of $S$ , it is intern... | {
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"seed": 7,
"temperature": 0.7
} | 7 | 7 | AIME24 | {
"expected_answer": "127",
"problem_id": "aime24-7",
"reference_rationale": null,
"reference_solution": "First, let's consider a section $\\mathcal{P}$ of the solids, along the axis.\nBy some 3D-Geomerty thinking, we can simply know that the axis crosses the sphere center. So, that is saying, the $\\mathcal... | To solve the problem, we need to determine the radii \( r_i \) and \( r_o \) of the circles along which the torus \( T \) is tangent to the sphere \( S \) when the torus is internally tangent (resting on the inside) and externally tangent (resting on the outside), respectively. Then, we will find the difference \( r_i ... |
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"content": "In this problem, the final will be a numeric value. Give the numerical answer correct upto the 2nd decimal digit. Give a detailed solution and end the solution with the final answer. Mark your solution with \\boxed\nAnswer:\n\nProblem: In a triangle $P Q R$, let $\\vec{a}=\\overrightarrow{Q R}, \\... | {
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"max_new_tokens": 32768,
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} | 2 | 274 | JEEBench | {
"expected_answer": "108",
"problem_id": "52",
"reference_rationale": null,
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"subject": "math",
"type": "Numeric"
} | To solve this problem, we need to find the value of \( |\vec{a} \times \vec{b}|^2 \) given the conditions on vectors \(\vec{a}\), \(\vec{b}\), and \(\vec{c}\) in triangle \(PQR\). Let's proceed step by step.
First, let's recall the given information:
1. In triangle \(PQR\), vectors are defined as:
- \(\vec{a} = \o... |
[
{
"content": "Your response should be in the following format:\nExplanation: {your explanation for your answer choice}\nAnswer: {your chosen answer}\nConfidence: {your confidence score between 0% and 100% for your answer}\nYou’re doing a laparoscopic appendectomy. You fire your stapler across the base of the ap... | {
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} | 1 | 500 | HLESubset | {
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"reference_rationale": "Taking a little cecum is easy, harmless, and happens often in an appendectomy. Best of all once you divide it, the appendix is now free and you can just pull out the stapler with the appendix attached.",
"reference_solut... | Explanation: When a laparoscopic stapler malfunctions during an appendectomy, the surgeon must quickly determine the best course of action to resolve the issue without compromising the patient's safety or the procedure's progress. The stapler not opening after firing is a critical complication that could lead to signif... |
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{
"content": "Problem: Define $f(x)=|| x|-\\tfrac{1}{2}|$ and $g(x)=|| x|-\\tfrac{1}{4}|$ . Find the number of intersections of the graphs of \\[y=4 g(f(\\sin (2 \\pi x))) \\quad\\text{ and }\\quad x=4 g(f(\\cos (3 \\pi y))).\\]\nMark your solution with \\boxed\nAnswer:",
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"seed": 7,
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} | 7 | 26 | AIME24 | {
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"problem_id": "aime24-26",
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"reference_solution": "If we graph $4g(f(x))$ , we see it forms a sawtooth graph that oscillates between $0$ and $1$ (for values of $x$ between $-1$ and $1$ , which is true because the arguments are between $-1$ and ... | To solve the problem, we need to find the number of intersections between the graphs of \( y = 4g(f(\sin(2\pi x))) \) and \( x = 4g(f(\cos(3\pi y))) \).
First, we need to understand the functions \( f(x) \) and \( g(x) \). Both are absolute value functions, which can be broken down into piecewise definitions.
### St... |
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"content": "Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.You are given two strings S and T consisting of lowercase English letters. Here, S and T have equal lengths.\nLet X be... | {
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} | To solve this problem, we need to transform string S into string T using the minimum number of operations, appending each intermediate step to an array X. The solution must also ensure that among all possible valid arrays with the minimum length, we choose the lexicographically smallest one.
### Approach
1. **Identify... |
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"content": "Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.A mayoral election is being held in AtCoder City. The candidates are Takahashi and Aoki.\nThere are N valid votes cast... | {
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} | To solve this problem, we need to determine if the outcome of the mayoral election between Takahashi and Aoki is already decided based on the current votes and the remaining votes to be counted. The key is to check whether one candidate's current lead is such that even if all remaining votes go to the other candidate, ... |
[
{
"content": "\"You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print th... | {
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} | 0 | 6 | CodeElo | {
"expected_answer": "",
"problem_id": "",
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} | Okay, let's tackle this problem. So, the task is to find the lexicographically smallest array possible by swapping elements that meet a certain condition. The condition is that when you swap a_i and a_j, their XOR must be less than 4.
Hmm, first, I need to understand what elements can be swapped. The XOR of two numbe... |
[
{
"content": "In this problem, the final will be a numeric value. Give the numerical answer correct upto the 2nd decimal digit. Give a detailed solution and end the solution with the final answer. Mark your solution with \\boxed\nAnswer:\n\nProblem: Consider the lines $\\mathrm{L}_1$ and $\\mathrm{L}_2$ defined... | {
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} | 1 | 332 | JEEBench | {
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"problem_id": "45",
"reference_rationale": null,
"reference_solution": null,
"subject": "math",
"type": "Numeric"
} | To solve this problem, we need to find the value of \(\lambda^2\) given the conditions described. Let's proceed step by step.
### Step 1: Determine the Loci of Points \(\mathrm{P}\)
First, we need to find the locus \(\mathrm{C}\) of points \(\mathrm{P}\) such that the product of their distances to \(\mathrm{L}_1\) an... |
[
{
"content": "Your response should be in the following format:\nExplanation: {your explanation for your answer choice}\nAnswer: {your chosen answer}\nConfidence: {your confidence score between 0% and 100% for your answer}\nWhat is the standard Japanese pitch accent pattern of 「弟」?\n\nAnswer Choices:\nA. Heiban\... | {
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"seed": 1,
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} | 1 | 19 | HLESubset | {
"expected_answer": "D",
"problem_id": "66e97fd756455f341c7849c3",
"reference_rationale": "「弟」(Hepburn Transliteration: otouto) is Japanese for \"younger brother\" and follows the Odaka (尾高) pitch accent pattern in standard Japanese. This can be verified in any source of pitch accent information, such as the “NH... | Explanation: The term "pitch accent" in Japanese refers to the pattern of stressed and unstressed syllables in a word, which can change the meaning or the register of the word. In the case of the Japanese word 「弟」, which means "brother," the standard pitch accent pattern is Heiban.
The options provided are:
A. Heiban... |
[
{
"content": "Generate an executable Python function generated from the given prompt. Return the function body without invoking it at the final solution.You are given an array nums of positive integers and an integer k.\nIn one operation, you can remove the last element of the array and add it to your collectio... | {
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} | 1 | 98 | LiveCodeBench | {
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} | To solve this problem, we need to determine the minimum number of operations required to collect all elements from 1 to k by removing elements from the end of the array. Each operation removes the last element of the array and adds it to our collection. The goal is to find the earliest point where all elements from 1 t... |
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{
"content": "Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.Given eight integers S_1,S_2,\\dots, and S_8,\r\nprint Yes if they satisfy all of the following three conditions, and ... | {
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"seed": 1,
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} | 1 | 227 | LiveCodeBench | {
"expected_answer": "",
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"subject": null,
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} | To solve this problem, we need to determine if a given sequence of eight integers meets three specific conditions. Let's break down each condition and how to check them:
1. **Monotonic Non-Decreasing**: Each element in the sequence must be greater than or equal to the previous one. This can be checked by iterating thr... |
[
{
"content": "Generate an executable Python function generated from the given prompt. Return the function body without invoking it at the final solution.Bob is stuck in a dungeon and must break n locks, each requiring some amount of energy to break. The required energy for each lock is stored in an array called... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
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} | 0 | 345 | LiveCodeBenchV5 | {
"expected_answer": "",
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} | To solve this problem, we need to determine the minimum time Bob requires to break all locks in a dungeon. The approach involves simulating the process of breaking each lock while considering the energy regeneration and factor adjustments. Here's a Python function that addresses the problem:
### Approach
1. **Initiali... |
[
{
"content": "You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print the ... | {
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} | 2 | 325 | CodeForces | {
"expected_answer": "",
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} | Okay, I need to solve this problem where I have to find the minimal disturbance after performing any number of swaps. The swaps allowed are swapping elements at positions i and n-i+1. Let's think about how to approach this.
First, the disturbance is the number of consecutive duplicates. The goal is to minimize this. T... |
[
{
"content": "Problem: Find the number of rectangles that can be formed inside a fixed regular dodecagon ( $12$ -gon) where each side of the rectangle lies on either a side or a diagonal of the dodecagon. The diagram below shows three of those rectangles. [asy] unitsize(0.6 inch); for(int i=0; i<360; i+=30) { d... | {
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"seed": 6,
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} | 6 | 14 | AIME24 | {
"expected_answer": "315",
"problem_id": "aime24-14",
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"reference_solution": "By Furaken There are two kinds of such rectangles: those whose sides are parallel to some edges of the regular 12-gon (Case 1), and those whose sides are not (Case 2). For Case 1, WLOG assume that the rect... | To find the number of rectangles that can be formed inside a regular dodecagon (12-gon) where each side of the rectangle lies on either a side or a diagonal of the dodecagon, we need to consider all possible rectangles that can be formed by selecting four vertices of the dodecagon such that the sides of the rectangle a... |
[
{
"content": "In this problem, the final answer will be a non-negative integer. Give a detailed solution and end the solution with the final answer. Mark your solution with \\boxed\nAnswer:\n\nProblem: A train with cross-sectional area $S_{t}$ is moving with speed $v_{t}$ inside a long tunnel of cross-sectional... | {
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"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 277 | JEEBench | {
"expected_answer": "9",
"problem_id": "2",
"reference_rationale": null,
"reference_solution": null,
"subject": "phy",
"type": "Integer"
} | \boxed{14}
To solve this problem, we need to analyze the flow of air around the train moving inside a tunnel. The key steps involve applying the principles of fluid dynamics, specifically Bernoulli's equation and the continuity equation, to relate the pressure difference caused by the train's motion to the velocity of... |
[
{
"content": "You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print the ... | {
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"seed": 2,
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} | 2 | 128 | CodeForces | {
"expected_answer": "",
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} | Okay, let's see. The problem is about calculating F(i) for each i, where F(i) is the number of black elements reachable from i. The key insight here is that the permutation forms cycles, and since the permutation is a bijection, each element is part of exactly one cycle. So, for any i, the reachable elements are all th... |
[
{
"content": "You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print the ... | {
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"max_new_tokens": 32768,
"seed": 2,
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} | 2 | 319 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_rationale": null,
"reference_solution": "",
"subject": null,
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} | Okay, I need to solve this problem where I have to count the number of pairs (i, j) such that when you remove a_i and a_j, the sum of the remaining elements is between x and y, inclusive. Hmm. Let's think about the approach.
The first thing I remember from the editorial is that the problem can be transformed into two ... |
[
{
"content": "Your response should be in the following format:\nExplanation: {your explanation for your answer choice}\nAnswer: {your chosen answer}\nConfidence: {your confidence score between 0% and 100% for your answer}\nLet $\\mathbb{R}, \\mathbb{C}$ represent the spaces of real and complex numbers, respect... | {
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"seed": 2,
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} | 2 | 28 | HLESubset | {
"expected_answer": "I",
"problem_id": "66eaa401c7a3252f0f3fe535",
"reference_rationale": "consider \n$$b(p)= \\underset{ \\left\\{ \\textbf{S} \\in \n \\textbf{SPD}_{7}:\\left[ \\sum_{i=1}^{7} \\lambda_i^2(f_2(\\textbf{S})) \\right] \\leq p^2 \\right\\}}{\\max} f_1(\\textbf{S}) \\\\\n$$\n\n\\begin{enumera... | Explanation: The problem involves computing an integral over p from 0 to infinity, where the integrand is a complex expression involving several functions and operations on matrices. The integrand is a ratio that combines exponential terms, powers of p, and a maximum over a set of matrices constrained by a condition. T... |
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{
"content": "Generate an executable Python function generated from the given prompt. Return the function body without invoking it at the final solution.You are given an integer array enemyEnergies denoting the energy values of various enemies.\nYou are also given an integer currentEnergy denoting the amount of... | {
"do_sample": false,
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"seed": 2,
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} | 2 | 93 | LiveCodeBenchV5 | {
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} | To solve this problem, we need to maximize the number of points gained by optimally choosing enemies to attack and defend in a strategic manner. The key is to balance the use of energy in a way that allows us to both attack and defend efficiently, considering the constraints on energy and the operations allowed.
### A... |
[
{
"content": "Problem: In $\\triangle{RST}$, shown, $\\sin{R}=\\frac{2}{5}$. What is $\\sin{T}$?\n\n[asy]\npair R,S,T;\nT = (0,0);\nS = (2,0);\nR = (2,sqrt(21));\ndraw(R--S--T--R);\ndraw(rightanglemark(R,S,T,10));\nlabel(\"$T$\",T,SW);\nlabel(\"$S$\",S,SE);\nlabel(\"$R$\",R,NE);\nlabel(\"$5$\",(R+T)/2,NW);\n[/... | {
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} | 0 | 389 | MATH500 | {
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} | To solve for $\sin{T}$ in $\triangle RST$ where $\sin{R} = \frac{2}{5}$, we can use the properties of right triangles and trigonometric identities.
First, since $\triangle RST$ is a right triangle, we can identify the right angle. The Asymptote code indicates a right angle at $S$, as marked by `rightanglemark(R,S,T,1... |
[
{
"content": "Generate an executable Python function generated from the given prompt. Return the function body without invoking it at the final solution.You are given an integer array nums and two positive integers m and k.\nReturn the maximum sum out of all almost unique subarrays of length k of nums. If no su... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
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} | 2 | 82 | LiveCodeBench | {
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} | To solve this problem, we need to find the maximum sum of an almost unique subarray of length k. An almost unique subarray is defined as one that contains at least m distinct elements.
### Approach
1. **Sliding Window Technique**: Use a sliding window approach to efficiently check each subarray of length k. This help... |
[
{
"content": "Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.You are given a sequence of N positive integers A = (A_1, A_2, \\dots ,A_N), where each element is at least 2. Anna an... | {
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"seed": 2,
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} | 2 | 118 | LiveCodeBenchV5 | {
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"reference_rationale": null,
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} | To solve this problem, we need to determine the winner of a game played by Anna and Bruno based on the given sequence of integers. The key insight is to analyze the game using the concept of Grundy numbers (or Nimbers) from combinatorial game theory, which helps in determining the winning strategy based on the game's s... |
[
{
"content": "Your response should be in the following format:\nExplanation: {your explanation for your answer choice}\nAnswer: {your chosen answer}\nConfidence: {your confidence score between 0% and 100% for your answer}\nA 64-year-old woman, para 4 gravida 1, arrives at a dermatology and plastic surgery group... | {
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"max_new_tokens": 32768,
"seed": 0,
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} | 0 | 144 | HLESubset | {
"expected_answer": "A",
"problem_id": "670c775842b25f65425c86c2",
"reference_rationale": "This patient's history of using alkylating agent chemotherapeutics (cyclophosphamide most likely for the ductal carcinoma) and bullae in the axilla are the main features that make the diagnosis lean towards malignancy-rela... | Explanation: The patient has several factors that point towards hidradenitis suppurativa. She is a 64-year-old woman with a BMI of 39, which is considered obese, and she smokes, which are risk factors for hidradenitis suppurativa. The lesions are located in the inframammary folds (axillary folds) and inguinal regions, ... |
[
{
"content": "In this problem, the final will be a numeric value. Give the numerical answer correct upto the 2nd decimal digit. Give a detailed solution and end the solution with the final answer. Mark your solution with \\boxed\nAnswer:\n\nProblem: Liquids $\\mathbf{A}$ and $\\mathbf{B}$ form ideal solution fo... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 291 | JEEBench | {
"expected_answer": "0.2",
"problem_id": "32",
"reference_rationale": null,
"reference_solution": null,
"subject": "chem",
"type": "Numeric"
} | To solve this problem, we need to determine the vapor pressure of pure liquid B at 25°C, given that liquids A and B form an ideal solution and that we have information about the total vapor pressures of two solutions with different compositions.
### Step-by-Step Solution:
1. **Understanding Ideal Solutions**:
- Fo... |
[
{
"content": "Your response should be in the following format:\nExplanation: {your explanation for your answer choice}\nAnswer: {your chosen answer}\nConfidence: {your confidence score between 0% and 100% for your answer}\nConsider the following two computational problems:\n\n1. $\\mathsf{DomSet}$.\nInput: A gr... | {
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"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 76 | HLESubset | {
"expected_answer": "C",
"problem_id": "66f760ebf206a49e129c7ed9",
"reference_rationale": "To avoid confusion: The answer is NOT B, since the second problem is on *counting* $\\ell$-independent sets, which is #W[1]-complete, and the connection between W[2] and #W[1] is not known.\n\nInstead, the only consequence... | Explanation: The problem involves computational complexity theory, specifically the relationship between parameterized complexity classes and the existence of certain algorithms. The key here is understanding the implications of an algorithm $\mathbb{A}$ for $\mathsf{DomSet}$ that uses an oracle for $\#\mathsf{IndSet}$... |
[
{
"content": "Return your final response within \\boxed{} and only include the letter choice (A, B, C, or D) as your final response.\nProblem: An organic chemist performs two reactions.\nReaction I:\n(S)-5-methoxyhexan-3-one is treated with LAH followed by an acidic workup.\nReaction II:\nPentane-2,4-dione is t... | {
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} | 1 | 125 | GPQADiamond | {
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} | B
Wait, no. Wait. Let me think through this step by step.
First, let's analyze Reaction I: (S)-5-methoxyhexan-3-one treated with LAH followed by an acidic workup.
(S)-5-methoxyhexan-3-one is a chiral molecule. When treated with LAH, it will reduce the ketone to an alcohol. Since it's (S)-configuration, the reduction... |
[
{
"content": "Generate an executable Python function generated from the given prompt. Return the function body without invoking it at the final solution.You are given an integer array nums and three integers k, op1, and op2.\nYou can perform the following operations on nums:\n\nOperation 1: Choose an index i an... | {
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"seed": 0,
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} | 0 | 326 | LiveCodeBenchV5 | {
"expected_answer": "",
"problem_id": "",
"reference_rationale": null,
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} | To solve this problem, we need to minimize the sum of all elements in the array after performing up to op1 operations of dividing by 2 (rounded up) and up to op2 operations of subtracting k (if possible). The key is to strategically apply these operations to the elements that will yield the maximum reduction in the sum... |
[
{
"content": "Your response should be in the following format:\nExplanation: {your explanation for your answer choice}\nAnswer: {your chosen answer}\nConfidence: {your confidence score between 0% and 100% for your answer}\nStarting with this initial array:\n\ninitial_array = [\n ['◬','◑'],\n ['◪','▨']\n]\... | {
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"max_new_tokens": 32768,
"seed": 0,
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} | 0 | 441 | HLESubset | {
"expected_answer": "E",
"problem_id": "673668e658bad7ba89d4ad54",
"reference_rationale": "The correct answer is:\n\nscale 2, roll 0 1, rotate clockwise, flip lr, transpose, scale 2, roll 1 2, rotate counterclockwise, flip ud, roll 0 3, antidiagonal_transpose, scale 2, rotate clockwise, roll 0 8, flip ud, roll 1... | Explanation:
The problem requires determining the sequence of commands that transforms the initial array into the given final array and identifying the hidden symbols at specific coordinates. The process involves applying a series of transformations (scale, roll, rotate, flip, transpose, antidiagonal_transpose) and t... |
[
{
"content": "\"You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print th... | {
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"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 134 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_rationale": null,
"reference_solution": "",
"subject": null,
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} | Okay, I need to solve this problem where I have to find the minimum number of operations to turn all cells white in an n x n grid. The grid is built such that each row has a_i cells black (from the first a_i cells) and the rest are white. The operations allowed are either dyeing a 2x2 subgrid white or dyeing an entire ... |
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{
"content": "In this problem, only one option will be correct. Give a detailed solution and end the solution with the final answer. Mark your solution, which should be exactly one multiple-choice letter, with \\boxed\nAnswer:\n\nProblem: An ideal gas is in thermodynamic equilibrium. The number of degrees of fr... | {
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"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 502 | JEEBench | {
"expected_answer": "C",
"problem_id": "21",
"reference_rationale": null,
"reference_solution": null,
"subject": "phy",
"type": "MCQ"
} | Okay, so I need to figure out which of the options A to D is correct based on the given information about an ideal gas in thermodynamic equilibrium. The key points here are the number of degrees of freedom (n), the internal energy (U_n), and the speed of sound (v_n) in the gas. The question is asking about the relation... |
[
{
"content": "Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.There is a road extending east and west, and N persons are on the road.\nThe road extends infinitely long to the east ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 138 | LiveCodeBenchV5 | {
"expected_answer": "",
"problem_id": "",
"reference_rationale": null,
"reference_solution": "",
"subject": null,
"type": null
} | To solve this problem, we need to determine the minimum total number of movements required for each task in the given sequence. Each task involves moving specific persons to their target positions, and we need to compute the cumulative movement steps for all tasks efficiently.
### Approach
1. **Understanding Movements... |
[
{
"content": "\"You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print th... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 53 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_rationale": null,
"reference_solution": "",
"subject": null,
"type": null
} | Okay, let's tackle this problem. So, the task is to find the longest common subsegment between two sequences generated by XOR operations with x and y. Hmm.
First, let's understand what the sequences look like. For a given n, a_n is n XOR x, and b_n is n XOR y. So, for each position n, we compute the XOR with x and y r... |
[
{
"content": "Return your final response within \\boxed{} and only include the letter choice (A, B, C, or D) as your final response.\nProblem: A common approximation made in many-body nuclear calculations of some interaction (for example an electroweak interaction) is to suppose that nucleons in a nucleus behav... | {
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"max_new_tokens": 32768,
"seed": 1,
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} | 1 | 19 | GPQADiamond | {
"expected_answer": "",
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} | D) 1,2,4
The impulse approximation in nuclear physics assumes that the interaction between nucleons is such that only the motion of an individual nucleon is considered, and the rest of the nucleus is "transparent" to the interaction except for the selected nucleon. This means that the interaction current only affects ... |
[
{
"content": "\"You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print th... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 359 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_rationale": null,
"reference_solution": "",
"subject": null,
"type": null
} | Okay, let's tackle this problem. Hmm, the problem is about determining after each query whether a permutation can be sorted using certain swap operations. The operations allowed are based on the characters in the string s. Each L allows a swap to the left (if possible), and each R allows a swap to the right (if possibl... |
[
{
"content": "Generate an executable Python function generated from the given prompt. Return the function body without invoking it at the final solution.You are given an integer n and a 0-indexed integer array sick which is sorted in increasing order.\nThere are n children standing in a queue with positions 0 t... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 146 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_rationale": null,
"reference_solution": "",
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} | To solve this problem, we need to determine the number of possible infection sequences for the children not initially infected. The key challenge is to model the possible sequences of infection based on the constraints given.
### Approach
1. **Identify Gaps**: The problem can be broken down into identifying the gaps b... |
[
{
"content": "\"You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print th... | {
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"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 176 | CodeElo | {
"expected_answer": "",
"problem_id": "",
"reference_rationale": null,
"reference_solution": "",
"subject": null,
"type": null
} | Okay, let's tackle this problem. Hmm, the problem is about selecting elements from array a, each time adding the value to the score and then subtracting the corresponding b_i from a_i. But after each operation, a_i can't go below zero. We need to maximize the score after exactly k operations.
So, the key here is to c... |
[
{
"content": "Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.Slavic is preparing a present for a friend's birthday. He has an array $a$ of $n$ digits and the present will be the p... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 1 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_rationale": null,
"reference_solution": "",
"subject": null,
"type": null
} | To solve this problem, we need to determine the maximum product of digits after incrementing exactly one digit by 1. The approach involves analyzing each digit in the array and calculating the potential product if that digit is increased by 1. However, we need to consider different cases to handle the edge cases correc... |
[
{
"content": "You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print the ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 148 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_rationale": null,
"reference_solution": "",
"subject": null,
"type": null
} | Okay, let's tackle this problem. So the task is to compute the alternating sum of a sequence of integers. The alternating sum starts with a plus, then minus, and so on. So for the example input like 1 2 3 17, the calculation would be 1 - 2 + 3 - 17. Let's see: 1-2 is -1, plus 3 is 2, minus 17 is -15. Which matches the ... |
[
{
"content": "You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print the ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 44 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_rationale": null,
"reference_solution": "",
"subject": null,
"type": null
} | Okay, I need to solve this problem where I have to generate a string of vowels (a, e, i, o, u) of length n such that the number of palindromic subsequences is minimized. Hmm. Let's think about how to approach this.
First, let's understand what makes a subsequence a palindrome. A palindrome reads the same forwards and ... |
[
{
"content": "In this problem, only one option will be correct. Give a detailed solution and end the solution with the final answer. Mark your solution, which should be exactly one multiple-choice letter, with \\boxed\nAnswer:\n\nProblem: Let $Q$ be the cube with the set of vertices $\\left\\{\\left(x_{1}, x_{2... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 454 | JEEBench | {
"expected_answer": "A",
"problem_id": "5",
"reference_rationale": null,
"reference_solution": null,
"subject": "math",
"type": "MCQ"
} | Alright, let's tackle this problem step by step. It's about finding the maximum distance between a line from set F (face diagonals) and a line from set S (space diagonals) of a cube Q. The cube has vertices at all combinations of 0 and 1 in each coordinate, so it's essentially a unit cube.
First, let's visualize the ... |
[
{
"content": "In this problem, the final answer will be a non-negative integer. Give a detailed solution and end the solution with the final answer. Mark your solution with \\boxed\nAnswer:\n\nProblem: Let $n \\geq 2$ be a natural number and $f:[0,1] \\rightarrow \\mathbb{R}$ be the function defined by\n\n$$\nf... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 458 | JEEBench | {
"expected_answer": "8",
"problem_id": "9",
"reference_rationale": null,
"reference_solution": null,
"subject": "math",
"type": "Integer"
} | \boxed{8}
To solve this problem, we need to determine the maximum value of the piecewise function \( f(x) \) defined on the interval \([0, 1]\). The problem states that the area under the curve \( f(x) \) between \( x = 0 \) and \( x = 1 \) is 4. Our goal is to find the value of \( n \) that satisfies this area condit... |
[
{
"content": "You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print the ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 383 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_rationale": null,
"reference_solution": "",
"subject": null,
"type": null
} | Okay, let's tackle this problem. Hmm. The problem is to find a sequence of operations that makes the array balanced. Each operation is choosing an index and adding 1 to the previous element, 2 to the current, and 1 to the next. And the array is cyclic. So the goal is to find v_1 to v_n where each v_i is the number of o... |
[
{
"content": "Problem: Roslyn has ten boxes. Five of the boxes contain pencils, four of the boxes contain pens, and two of the boxes contain both pens and pencils. How many boxes contain neither pens nor pencils?\nMark your solution with \\boxed\nAnswer:",
"role": "user"
}
] | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 404 | MATH500 | {
"expected_answer": "",
"problem_id": "",
"reference_rationale": null,
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"subject": null,
"type": null
} | To solve this problem, we need to determine how many boxes contain neither pens nor pencils. Let's start by understanding the given information:
- Total number of boxes: 10
- Number of boxes with pencils: 5
- Number of boxes with pens: 4
- Number of boxes with both pens and pencils: 2
First, we need to find out how m... |
[
{
"content": "You are a coding expert. Given a competition-level coding problem, you need to write a Python program to solve it. You may start by outlining your thought process. In the end, please provide the complete code in a code block enclosed with ``` ```. The code should take stdin as input and print the ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
} | 2 | 224 | CodeForces | {
"expected_answer": "",
"problem_id": "",
"reference_rationale": null,
"reference_solution": "",
"subject": null,
"type": null
} | Okay, I need to solve this problem where I have to handle dynamic set operations and compute the k-load efficiently. Let's think about how to approach this.
The problem requires supporting three operations: insert, remove, and query the k-load. The k-load is the minimum d such that there's a gap of k consecutive numbe... |
[
{
"content": "Generate an executable Python function generated from the given prompt. Return the function body without invoking it at the final solution.You are given a 1-indexed array of distinct integers nums of length n.\nYou need to distribute all the elements of nums between two arrays arr1 and arr2 using ... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 189 | LiveCodeBench | {
"expected_answer": "",
"problem_id": "",
"reference_rationale": null,
"reference_solution": "",
"subject": null,
"type": null
} | To solve this problem, we need to distribute elements of an array into two subarrays, `arr1` and `arr2`, based on a specific comparison rule. The goal is to determine the final concatenated result after all operations.
### Approach
1. **Initialization**: Start by initializing two arrays, `arr1` and `arr2`, with the fi... |
[
{
"content": "In this problem, multiple options can be correct. Give a detailed solution and end the solution with the final answer. Mark your solution, which should be one or more multiple-choice letter(s), with \\boxed\nAnswer:\n\nProblem: Let $f:(0, \\infty) \\rightarrow \\mathbb{R}$ be a differentiable func... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
} | 0 | 30 | JEEBench | {
"expected_answer": "A",
"problem_id": "43",
"reference_rationale": null,
"reference_solution": null,
"subject": "math",
"type": "MCQ(multiple)"
} | Alright, let's tackle this problem step by step. We have a differentiable function \( f:(0, \infty) \rightarrow \mathbb{R} \) that satisfies the differential equation \( f'(x) = 2 - \frac{f(x)}{x} \) for all \( x \in (0, \infty) \), and we know that \( f(1) \neq 1 \). Our goal is to determine which of the given stateme... |
[
{
"content": "Problem: Torus $T$ is the surface produced by revolving a circle with radius $3$ around an axis in the plane of the circle that is a distance $6$ from the center of the circle (so like a donut). Let $S$ be a sphere with a radius $11$ . When $T$ rests on the inside of $S$ , it is intern... | {
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
} | 1 | 7 | AIME24 | {
"expected_answer": "127",
"problem_id": "aime24-7",
"reference_rationale": null,
"reference_solution": "First, let's consider a section $\\mathcal{P}$ of the solids, along the axis.\nBy some 3D-Geomerty thinking, we can simply know that the axis crosses the sphere center. So, that is saying, the $\\mathcal... | To solve this problem, we need to determine the radii of the circles along which the torus is tangent to the sphere when it is both internally and externally tangent, and then find the difference between these radii.
### Step 1: Understanding the Torus
A torus generated by revolving a circle with radius \(3\) around a... |
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